CP violation in the decays of neutral kaons into two photons

Abstract

We compute the amplitudes for the decay into two photons of neutral kaons in the framework of the chiral effective Lagrangians. In particular we relate the ratios\(\eta _{||} = A(K_L \to 2\gamma _{||} )/A(K_S \to 2\gamma _{||} )\) and\(\eta _ \bot = A(K_S \to 2\gamma _ \bot )/A(K_L \to 2\gamma _ \bot ),\) which would vanish according toCP symmetry, to the prameters ɛ and ɛ′, appearing in the 2π decays ofKL. We find for\(\eta _{||} \) the value ɛ+i|ɛ′|. For the amplitudes into\(2\gamma _ \bot ,\), theCP-conserving amplitude\(A(K_2 \to 2\gamma _ \bot )\) depends very strongly on the parameterf, which gives the percentage of the amplitude\(A(K_2 \to 2\pi ^0 )\) arising from the «penguin» contributions. We predict two possible values for\(\eta _ \bot \): one is ≃ɛ. For the other =ɛ+i70|ɛ′|, which appears to us as more likely, the difference with respect to the superweak theory is larger than in the 2π decays. A distinction between the two theories requires a more precise measurement of γ(KS»γγ).